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Spec links: 4.5.4 Moments, levers and gears (Physics only) · Reading time: about 4 minutes

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The nut that would not move

Maya’s bike has a flat tyre. To take the wheel off, she has to undo a nut. She grips it with her fingers and twists. Nothing. She tries a tiny spanner. Still nothing. Then her gran hands her a long spanner. With one push, the nut turns. Maya has not suddenly become stronger. She has used physics.

The turning effect of a force

A force can make an object turn about a fixed point. This point is called the pivot. The turning effect of a force is called its moment. We calculate it using M = F d.

M is the moment in newton-metres (N m). F is the force in newtons (N). d is the perpendicular distance from the pivot to the line of action of the force, in metres (m). “Perpendicular” means at right angles. You get the biggest moment when you push at right angles to the spanner.

Suppose Maya pushes with a force of 60 N on the end of a spanner 0.25 m long. The moment is M = 60 × 0.25 = 15 N m. The small spanner was only 0.10 m long. To get the same 15 N m with it, she would need F = M ÷ d = 15 ÷ 0.10 = 150 N. A longer spanner means a bigger distance, so a smaller force gives the same turning effect.

Levers and balanced beams

A spanner is a type of lever. Levers include crowbars, wheelbarrows, scissors and even bottle openers. A lever acts as a force multiplier. A small force applied far from the pivot can produce a large force close to the pivot.

Now think about a seesaw. If it is balanced, the principle of moments applies. The total clockwise moment about the pivot equals the total anticlockwise moment about the pivot.

Maya weighs 450 N and sits 2.0 m from the pivot. Her anticlockwise moment is 450 × 2.0 = 900 N m. Her little brother weighs 300 N. Where must he sit to balance her? His clockwise moment must also be 900 N m, so d = 900 ÷ 300 = 3.0 m. The lighter person must sit further from the pivot.

Gears on a bike

Once the tyre is fixed, Maya rides up a steep hill. She clicks into a low gear. Gears are wheels with teeth that lock together, or that are linked by a chain. They transmit the rotational effect of a force from one place to another.

On a bike, the chain pulls on the teeth of the rear gear. The force from the chain acts at the edge of the gear, so the moment depends on the gear’s radius. When a force is passed to a larger gear, the moment is bigger, but the gear turns more slowly. Climbing a hill, Maya uses a large rear gear. The chain gives a bigger moment on the back wheel, so pedalling is easier, but she moves more slowly. On a flat road she switches to a small rear gear. Each push needs more effort, but the wheel turns faster.

Spanners, seesaws and gears all depend on the same idea. Turning effect depends on both force and distance.

Key words

• Moment: the turning effect of a force, calculated as force × perpendicular distance from the pivot; measured in N m.
• Pivot: the fixed point about which an object turns.
• Perpendicular distance: the distance from the pivot to the line of action of the force, measured at right angles to that line.
• Principle of moments: if an object is balanced, the total clockwise moment about a pivot equals the total anticlockwise moment about that pivot.
• Lever: a simple machine that acts as a force multiplier by applying a force at a distance from a pivot.
• Gears: toothed wheels that transmit the rotational effect of forces.

Questions

1. What is the name given to the turning effect of a force? [1 mark]
2. Name two examples of levers given in the article. [2 marks]
3. State the principle of moments. [2 marks]
4. Explain why it is easier to undo a tight nut with a long spanner than with a short one. [2 marks]
5. Explain why a cyclist uses a large rear gear to ride up a steep hill. [3 marks]
6. A mechanic pushes at right angles on the end of a wrench with a force of 80 N. The distance from the nut to where she pushes is 0.35 m. Calculate the moment of the force. Give the unit. [3 marks]
7. A seesaw is balanced. A child of weight 360 N sits 1.5 m from the pivot. An adult of weight 720 N sits on the other side. Calculate how far from the pivot the adult is sitting. [3 marks]
8. A wheelbarrow, a spanner and a bicycle all use moments. Explain how forces and moments make each of these easier to use. [6 marks]

Show answers

1. Moment (1)
2. Any two from: spanner; crowbar; wheelbarrow; scissors; bottle opener; seesaw (1 each, max 2)
3. If an object is balanced (1); the total clockwise moment about a pivot equals the total anticlockwise moment about that pivot (1)
4. The longer spanner gives a greater (perpendicular) distance from the pivot (1); so the same force gives a bigger moment / a smaller force is needed for the same moment (1)
5. The chain’s force acts at a larger radius / greater distance from the centre of the gear (1); so the moment on the back wheel is bigger (1); so less force is needed on the pedals / pedalling is easier (but the wheel turns more slowly) (1)
6. M = F d = 80 × 0.35 (1); M = 28 (1); N m (1)
7. Clockwise moment = anticlockwise moment, so 360 × 1.5 = 720 × d (1); 540 = 720 × d, so d = 540 ÷ 720 (1); d = 0.75 m (1)
8. Indicative content: moment = force × perpendicular distance from the pivot; wheelbarrow: the wheel is the pivot; handles are far from the pivot and the load is close to it; a small upward force on the handles gives a moment equal to the moment of the much heavier load; wheelbarrow acts as a force multiplier; spanner: the nut is the pivot; a long handle increases the distance; a small force produces a large moment to turn the nut; pushing at right angles gives the greatest moment; bicycle: pedals and cranks act as levers about the axle; gears transmit the rotational effect; a larger rear gear gives a bigger moment on the wheel, making hills easier but the wheel turns more slowly; a smaller rear gear makes the wheel turn faster but needs more force.
   Level 3 (5–6 marks): a clear explanation for all three examples, each linking distance from the pivot to the size of the moment and the force needed; Level 2 (3–4 marks): explanation for at least two examples with some correct links between force, distance and moment; Level 1 (1–2 marks): simple statements, e.g. “a longer handle makes it easier”, with little explanation.

More reading: See all 30 GCSE Physics comprehension articles